Low-noise fiber optic sensor utilizing a laser source

ABSTRACT

A fiber-optic sensor includes an optical fiber coil and a laser source optically coupled to the coil. Light from the source is transmitted to the coil as a first signal propagating along the coil in a first direction and a second signal propagating along the coil in a second direction opposite to the first direction. The optical paths of the first signal and the second signal are substantially reciprocal with one another and the first signal and the second signal are combined together after propagating through the coil to generate a third signal. The laser source is frequency-modulated or can have a coherence length longer than a length of the coil.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to U.S. ProvisionalApplication No. 60/988,404, filed Nov. 15, 2007, which is incorporatedin its entirety by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This application relates generally to fiber-optic sensors, and moreparticularly, to fiber-optic gyroscopes.

2. Description of the Related Art

Early experimental demonstrations of the fiber-optic gyroscope (FOG)were obtained using a laser for the optical source. See, e.g., R. A.Bergh, H. C. Lefèvre, and H. J. Shaw, “All-single-mode fiberopticgyroscope,” Optics Letters, vol. 6, no. 4, pp. 198-200 (1981).Shot-noise-limited sensitivity for the FOG was expected (see, e.g., H.C. Lefèvre, “The Fiber-Optic Gyroscope,” Artech House, Inc., Norwood,Mass. (1993)), but it was actually observed that the sensitivity wasdramatically deteriorated by backscattering in the optical fiber (see,e.g., C. C. Cutler, S. A. Newton, and H. J. Shaw, “Limitation ofrotation sensing by scattering,” Optics Letters, vol. 5, no. 11, pp.488-490 (1980)). The replacement of the laser by a superfluorescentsource (SFS) (see, e.g., K. Böhm, P. Marten, K. Petermann, E. Weidel,and R. Ulrich, “Low-drift fibre gyro using a superluminescent diode,”Electronics Letters, vol. 17, no. 10, pp. 352-353 (1981)) offered adramatic reduction of this backscattering-induced noise, along with areduction of other sources of noise due to the Kerr effect, polarizationfluctuations, and the Faraday effect.

SUMMARY OF THE INVENTION

In certain embodiments, a fiber-optic sensor comprises an optical fibercoil and a frequency-modulated laser source optically coupled to thecoil. Light from the source is transmitted to the coil as a first signalpropagating along the coil in a first direction and a second signalpropagating along the coil in a second direction opposite to the firstdirection. The optical paths of the first signal and the second signalare substantially reciprocal with one another and the first signal andthe second signal are combined together after propagating through thecoil to generate a third signal.

In certain embodiments, a method operates a fiber-optic sensor. Themethod comprises providing a fiber-optic sensor comprising an opticalfiber coil and a laser source optically coupled to the coil. The methodfurther comprises transmitting light from the source to the coil as afirst signal and a second signal. The first signal propagates along thecoil in a first direction and the second signal propagates along thecoil in a second direction opposite to the first direction. The opticalpaths of the first signal and the second signal are substantiallyreciprocal with one another. The method further comprises combining thefirst signal and the second signal together to generate a third signal.The method further comprises modulating a frequency of the laser sourcesuch that the first signal and the second signal arefrequency-modulated.

In certain embodiments, a fiber-optic sensor comprises a coil of opticalfiber having a length and a laser source optically coupled to the coil.The laser source has a coherence length longer than the length of thecoil fiber. Light from the source is transmitted to the coil as a firstsignal propagating along the coil in a first direction and a secondsignal propagating along the coil in a second direction opposite to thefirst direction. The optical paths of the first signal and the secondsignal are substantially reciprocal with one another and the firstsignal and the second signal are combined together after propagatingthrough the coil to generate a third signal.

In certain embodiments, a method operates a fiber-optic sensor. Themethod comprises providing a fiber-optic sensor comprising a coil ofoptical fiber having a length and a laser source optically coupled tothe coil. The laser source has a coherence length longer than the lengthof the coil fiber. The method further comprises transmitting light fromthe source to the coil as a first signal and a second signal. The firstsignal propagates along the coil in a first direction and the secondsignal propagates along the coil in a second direction opposite to thefirst direction. The optical paths of the first signal and the secondsignal are substantially reciprocal with one another. The method furthercomprises combining the first signal and the second signal together togenerate a third signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example fiber-optic sensor 10 inaccordance with certain embodiments described herein.

FIG. 2 schematically illustrates a single scatterer S in the opticalfiber coil of a Sagnac fiber-optic sensor in accordance with certainembodiments described herein.

FIG. 3A is a plot of a linearly swept frequency of the laser source inaccordance with certain embodiments described herein.

FIG. 3B is a plot of the shifted frequencies of the backscattered andmain signals in accordance with certain embodiments described herein.

FIG. 4 is a plot of the dependence of the beat frequency of thebackscattered noise with the scatterer position in accordance withcertain embodiments described herein.

FIG. 5A is a plot of the optical linewidth of the laser source inaccordance with certain embodiments described herein.

FIG. 5B is a plot of the electrical linewidth of the beat signal inaccordance with certain embodiments described herein.

FIGS. 5C-5E illustrate the proper frequency f₀ and the beat frequencyΔv_(B) for various levels of coherence of the laser source.

FIG. 6A is a plot of a periodic sawtooth frequency modulation waveformshape in accordance with certain embodiments described herein.

FIG. 6B is a plot of the returning optical frequencies and the beatfrequencies for a periodic frequency modulation in accordance withcertain embodiments described herein.

FIG. 7 is a plot of the density of probability of a sawtooth waveformand of a sine waveform.

FIGS. 8A and 8B schematically illustrate two example sensors inaccordance with certain embodiments described herein.

FIG. 9 is a plot of the rotation signal for the sensor of FIG. 8A with aSMF-28 fiber for three different optical sources: a SFS, a laser, and afrequency-modulated laser.

FIG. 10 is a plot of the RF spectra observed for the sensor of FIG. 8Awith a SMF-28 fiber at rest.

FIG. 11 is a plot of the RF spectra observed for the sensor of FIG. 8Awith an air-core optical fiber at rest.

FIGS. 12A and 12B illustrate some temporal and spectral characteristicsof the detector signal for the air-core FOG at rest.

FIG. 13 illustrates the dependence of the noise on the square root ofthe detection bandwidth for a standard fiber coil.

FIG. 14 schematically illustrates an example sensor in accordance withcertain embodiments described herein.

FIG. 15 is a flow diagram of an example method of operating afiber-optic sensor in accordance with certain embodiments describedherein.

FIG. 16 shows the results of a numerical theoretical model of certainembodiments utilizing a source coherence length greater than the coillength.

FIG. 17 is a flow diagram of an example method of operating afiber-optic sensor in accordance with certain embodiments describedherein.

DETAILED DESCRIPTION

Broadband sources, such as super-fluorescent sources (SFSs), arecommonly used for fiber-optic sensors such as fiber-optic gyroscopes(FOGs) in order to reduce deleterious effects related to the Kerr andFaraday effects, polarization-related non-reciprocity, and noise arisingfrom coherent backscattering. While use of an SFS as the light sourcehas resulted in notable improvements of the sensitivity of the FOG, thesensitivity is still limited by two main disadvantages. One additionalsource of noise related to the use of a broadband source is theexcess-noise due to the beating between the different spectralcomponents of the broadband source at the detector, unless specificexcess-noise reduction techniques are used. See, e.g., R. P. Moeller andW. K. Burns, “1.06-μm all-fiber gyroscope with noise subtraction,”Optics Letters, vol. 16, no. 23, pp. 1902-1904 (1991) and U.S. Pat. No.5,530,545, which is incorporated in its entirety by reference herein.Another drawback of the SFS as a light source for the FOG is thedifficulty in stabilizing the mean wavelength of the SFS's broadbandoutput. These drawbacks have contributed to the prevention of the FOGfrom being used in aircrafts as the sole inertial navigation instrument.

FIG. 1 schematically illustrates an example fiber-optic sensor 10 inaccordance with certain embodiments described herein. The sensor 10comprises an optical fiber coil 20 and at least one optical coupler 30optically coupled to the coil 20. The sensor 10 further comprises afrequency-modulated laser source 40 optically coupled to the at leastone optical coupler 30. Light from the laser source 40 is transmitted bythe at least one optical coupler 30 to the coil 20 as a first signal 52propagating along the coil 20 in a first direction 54 and a secondsignal 56 propagating along the coil 20 in a second direction 58opposite to the first direction 54. The optical paths of the firstsignal 52 and the second signal 56 are substantially reciprocal with oneanother and the first signal 52 and the second signal 56 are combinedtogether by the at least one optical coupler 30 to generate a thirdsignal 60.

In certain embodiments, the fiber-optic sensor 10 is a Sagnac-basedfiber-optic sensor, as schematically illustrated by FIG. 1. The sensor10 of certain embodiments is a FOG that is sensitive to rotations of thecoil 20 (e.g., the power carried by the third signal 60 changes as therate of rotation (e.g., in degrees per hour) applied to the coil 20varies). In certain other embodiments, the sensor 10 is configured to besensitive to one or more other perturbations, including but not limitedto, acoustic, thermal, and magnetic perturbations. The sensor 10 ofcertain embodiments thereby provides for detection of one or more of thefollowing: rotational movements, acoustic fields, thermal transients,and magnetic fields. The sensor 10 of certain embodiments is configuredto be used for one or more purposes, including but not limited to, as acompass, as a gyrocompass, and as a motion sensor. Persons skilled inthe art will recognize that while the majority of the discussion belowis presented with regard to FOGs, other fiber-optic sensors are alsocompatible with certain embodiments described herein.

The coil 20 of certain embodiments comprises a plurality ofsubstantially concentric loops. In certain embodiments, the coil 20comprises a conventional optical fiber (e.g., a single-mode fiber suchas the SMF-28® optical fiber available from Corning, Inc. of Corning,N.Y.). In certain other embodiments, the coil 20 comprises an air-coreoptical fiber (e.g., a hollow-core photonic bandgap fiber such as theHC-1550-02 optical fiber available from Crystal Fibre A/S of Birkerød,Denmark). In certain embodiments, the air-core optical fiberadvantageously provides a reduction of one or more of the Kerr effect,the Faraday effect, and the Shupe (thermal) effect, as compared toconventional optical fibers. See, e.g., U.S. Pat. Appl. Publ. No.2008/0030741 A1 and H. K. Kim, V. Dangui, M. Digonnet, and G. Kino,“Fiber-optic gyroscope using an air-core photonic-bandgap fiber,”Proceedings of the SPIE, vol. 5855, no. 1, pp. 198-201 (2005), each ofwhich is incorporated in its entirety by reference herein. However, thebackscattering coefficient of existing air-core optical fibers isactually higher than that in conventional solid-core optical fibers (byup to about one order of magnitude), thereby severely limiting thesensitivity of a laser-driven air-core fiber-optic sensor (e.g., FOG).However, with straightforward technical improvements, air-core opticalfibers can have a dramatically reduced backscattering level which ismuch lower than prevails in current air-core fibers. For example, onemethod for reducing backscattering of an air-core optical fiber is toincrease the diameter of the fiber core, e.g., by removing 19 tubes fromthe fiber preform to form the core, rather than 7 as is done for mostcurrent air-core optical fibers. A second method includes designing thefiber such that it has a wider bandgap. This can be accomplished, forexample, by increasing the fiber's air-filling ratio. A third approachfor reducing the level of backscattering is to increase the speed atwhich the fibers are drawn, which in itself requires adjusting otherfabrication and preform parameters, such as the temperature of the meltzone, the pressure of the gas applied to the preform's tubes, theviscosity and/or composition of the glass, etc. These methods ofreducing backscattering in an air-core optical fiber, and their physicalorigin and mathematical justifications (in some cases), can be found inVinayak Dangui's Doctorate Thesis, Laser-Driven Air-CorePhotonic-Bandgap Fiber Optic Gyroscope, Electrical EngineeringDepartment, Stanford University, October 2007, in particular in Section5.3.7, which is incorporated in its entirety by reference herein. Otheroptical fibers are also compatible with various embodiments describedherein.

In certain embodiments, as schematically illustrated by FIG. 1, the atleast one optical coupler 30 comprises a first optical coupler 70comprising a first port 72, a second port 74, and a third port 76. Forexample, the first optical coupler 70 can comprise a 3-dB opticalcoupler, as schematically illustrated in FIG. 1. The first opticalcoupler 70 of certain embodiments comprises additional ports. In certainembodiments, the second port 74 is optically coupled to a first end 22of the coil 20 and the third port 76 is optically coupled to a secondend 24 of the coil 20, as schematically illustrated by FIG. 1. Lightgenerated by the laser source 40 received at the first port 72 is splitinto the first signal 52 and the second signal 56. The first signal 52is transmitted by the second port 74 to the first end 22 of the coil 20to propagate in the first direction 54 (e.g., clockwise) along the coil20, and is transmitted by the second end 24 of the coil 20 and the thirdport 76 to the first port 72. The second signal 56 is transmitted by thethird port 76 to the second end 24 of the coil 20 to propagate in thesecond direction 58 (e.g., counterclockwise) along the coil 20, and istransmitted by the first end 22 of the coil 20 and the second port 74 tothe first port 72. Thus, the first signal 52 and the second signal 56counterpropagate through the coil 20 and are recombined together by thefirst optical coupler 70.

In such a configuration, the optical paths of the first signal 52 andthe second signal 56 are substantially reciprocal with one another. Theterm “reciprocal” as used herein includes its broadest reasonableinterpretation, including, but not limited to, optical paths which havesubstantially the same optical length and which have substantially equalresponses to perturbations (e.g., thermal variations). For example, forlight traveling from a first state (“state” including polarizationstate, phase, but not amplitude) at point A to a second state at pointB, light propagation is reciprocal if upon reversing the direction oflight at point B, the light (now starting in the second state at pointB) gets back to point A again in the first state. For certainembodiments described herein, because the two signals 52, 56 travelalong the same optical path, their propagation is basically orsubstantially reciprocal such that the phase accumulated by the firstsignal 52 as it travels around the entire coil 20 in one direction isequal to the phase accumulated by the second signal 56 as it travelsaround the entire coil 20 in the opposite direction. This reciprocitywould be absolute in the absence of nature's very few non-reciprocaleffects, such as the Faraday effect (resulting from exposure to amagnetic field) and the Sagnac effect (resulting from exposure to arotation), and in the absence of asymmetric time-dependent effects (suchas dynamic perturbations, e.g., pressure or temperature variations),applied asymmetrically to any fraction or all of the sensing coil 20.However, this reciprocity is not absolute unless nonreciprocal effectsare all exactly zero, which means, in particular, that the two signals52, 56 must be in the same state of polarization (SOP) at every pointalong the coil 20 (although the SOP of each signal does not have to bethe same at every point along the coil 20). In this context, the term“substantially reciprocal” recognizes that canceling these residualnon-reciprocal effects is never complete. Examples of systems comprisingsubstantially reciprocal optical paths include, but are not limited to,common-path interferometers and common-mode interferometers. Examples ofnon-reciprocal optical paths are found in J. Zheng, “All-fibersingle-mode fiber frequency-modulated continuous-wave Sagnac gyroscope,”Optics Letters, Vol. 30, pp. 17-19 (2005) which discloses an unbalancedinterferometer.

In certain embodiments, as schematically illustrated by FIG. 1, the atleast one optical coupler 30 further comprises a second optical coupler80 comprising a first port 82, a second port 84, and a third port 86.The second optical coupler 80 of certain embodiments comprisesadditional ports. For example, the second optical coupler 80 cancomprise an optical circulator, as schematically illustrated by FIG. 1.In certain embodiments, the first port 82 receives light generated bythe laser source 40 (e.g., the first port 82 is optically coupled to thelaser source 40), the second port 84 is optically coupled to the firstport 72 of the first optical coupler 70, and the third port 86 isoptically coupled to a detection system 90. Light received by the firstport 82 from the laser source 40 is transmitted through the second port84 to the first port 72 of the first optical coupler 70. Light (e.g.,the third signal 60) received by the second port 84 from the first port72 of the first optical coupler 70 is transmitted through the third port86 to the detection system 90. Other configurations of the at least oneoptical coupler 30 are also compatible with certain embodimentsdescribed herein. For example, the at least one optical coupler 30 cancomprise additional or fewer optical elements, and the second opticalcoupler 80 can comprise a 3-dB optical coupler. As described more fullybelow, in certain embodiments, the sensor 10 can comprise a polarizerwhich can be used advantageously to achieve polarization reciprocity.

When the coil 20 is not rotated, the first signal 52 and the secondsignal 56 returning to the first port 72 after propagating through thecommon-path interferometer formed by the coil 20 and the first coupler70 are recombined in phase. If a dynamic perturbation is applied to thecoil 20 anywhere but in the mid-point of the coil 20 (identified by asmall cross on the coil 20 of FIG. 1), the counterpropagating firstsignal 52 and second signal 56 experience a phase differential. When thetwo signals 52, 56 are recombined by the at least one optical coupler 30at the port 72, this phase differential results in an amplitudedifferential in the third signal 60 at the port 72, which is detected bythe detector system 90. This amplitude differential contains theinformation about the perturbation. A rotation of the coil 20 alsoinduces a phase shift whose amplitude is proportional to the rotationrate. When the sensor 10 is not perturbed (e.g., when the FOG is withoutrotation), the signal returning from an ideal FOG contains spectralcomponents at even multiples of the modulation frequency (dc included),but does not return any signal at f₀. However, any perturbation,including backscattering noise, will induce a component at f₀. Thus, thesignal of interest in certain embodiments is modulated at f₀.

In certain embodiments, the laser source 40 has a mean wavelength in arange between about 1.48 μm and about 1.6 μm. The mean wavelength of thelaser source 40 of certain embodiments is stable to within about onepart per million or better. The greater stability of the mean wavelengthof certain embodiments, as compared to an SFS, advantageously provides agreater scale-factor stability for the FOG. In certain embodiments, thelaser source 40 comprises a laser having a narrow bandwidth such thatits coherence length is equal to the length of the coil 20 or less. Incertain embodiments, the bandwidth of the laser source 40 issufficiently narrow such that the sensor 10 is substantially free fromexcess noise due to beating between the spectral components of the lasersource 40 (e.g., the excess noise is below the shot noise of thedetected signal). Examples of lasers compatible with certain embodimentsdescribed herein include, but are not limited to, external-cavitysemiconductor diode lasers and distributed feedback fiber lasers. Incertain embodiments, the distributed-feedback fiber laser is moresuitable since it is more compact and robust than an external-cavitysemiconductor diode laser. In certain embodiments, the laser frequencyis modulated in some pattern (e.g., sinusoidal, saw-tooth, etc.) at aselected frequency f_(m).

Coherent backscattering due to the interaction between light andinhomogeneities in the local index of refraction of a medium is known tobe a primary noise source in a variety of Sagnac interferometer-basedsensors such as fiber optic gyroscopes, acoustic sensors, etc. Whenlight encounters such a local inhomogeneity, it is scattered in variousdirections. The portion of the scattered light in the reverse directionthat is within the acceptance cone of the fiber will couple into thereverse propagating mode. Upon exiting the coil, this light willinterfere with each of the primary waves, producing an error signal. Theoptical paths of the scattered light and the primary light are no longerreciprocal, so that local variations in the fiber propagation constantdue to temperature transients or fluctuating magnetic fields, as well asphase fluctuations in the source will cause the error signal due tobackscattering to fluctuate in time when the interference that occurs iscoherent. The root mean square (RMS) fluctuations in this error signallimit the minimum sensitivity of Sagnac-loop-based sensors such as theFOG. In the case of the FOG, this type of noise is often characterizedby the FOG random walk, given in units of deg/√hr.

In certain embodiments, the frequency-modulated laser source 40advantageously provides a reduction of the excess noise (and thusimproved sensitivity, e.g., to rotation for a FOG), and in certainembodiments, provides a reduction of the backscattered noise. FIG. 2schematically illustrates a single scatterer S at a position z in theoptical fiber coil 20 of a Sagnac fiber-optic sensor 10 in accordancewith certain embodiments described herein. The coil 20 schematicallyillustrated by FIG. 2 includes a phase modulator 130, as described morefully below. In certain embodiments, the phase modulator 130 biases theinterferometer in quadrature, as described in H. C. Lefèvre, “TheFiber-Optic Gyroscope,” Artech House, Inc., Norwood, Mass. (1993). Thesensor 10 of FIG. 2 is an example of a fiber-optic gyroscope comprisinga standard Sagnac loop, which comprises a coil 20 closed upon itself byan optical coupler, e.g., a 3-dB fiber coupler. In certain embodiments,the period of the phase modulation by the phase modulator 130 is twicethe time-of-flight in the coil 20, and the frequency of this phasemodulation is referred to as the proper frequency f₀ of the sensor 100.In certain embodiments, the modulation frequency of the phase modulator130 is equal to the proper frequency f₀ of the coil 20. This selectionof frequency has a number of advantageous benefits, including maximizingthe sensitivity of the FOG to rotation, as described by H. C. Lefèvre,cited above. Another beneficial effect of this phase modulation is thatwhen the coil is rotated, the interference signal caused by thisrotation at the output of the coil is centered at frequency f₀.

Backscattering noise arises from the interaction at the detector of thefirst signal 52 and the generally weaker signal generated bybackscattering of the second signal 56 off scatterers (e.g., thescatterer S at position z). The small amount of backscattered lighttravels back to the at least one optical coupler 30, where it interfereswith the first signal 52, thus generating noise on the first signal 52(due to the random character of both the phase of the photons in thefirst signal 52 and the phase and amplitude of the reflection off thescatterer). Since in this direction, by the time they interact both thefirst signal 52 and the backscattered signal have traveled through thephase modulator 130, the spurious signal resulting from theirinterference occurs at frequency f₀. Since the rotation-induced signalon the FOG output signal also occurs at f₀ (see, H. C. Lefèvre, citedabove), this spurious signal is indistinguishable from the rotationsignal of the FOG, and it therefore constitutes a source of error. Inthe opposite direction, the main difference, in the example sensor 10 ofFIG. 2, is that by the time the second signal 56 and the backscatteredsignal due to backscattering of the first signal 52 off scatterersinteract, only the second signal 56 has traveled through the phasemodulator 130. The reason is two fold. First, the backscattered signalwas generated from the first signal 52 backscattering from the scattererat position z, which occurs at a time when the first signal 52 had notyet traveled through the phase modulator 130 and thus had not yet beenmodulated. Second, because this particular backscattered signal travelscounterclockwise, it also never travels through the phase modulator 130.As a result, in this particular configuration, the second signal 56 doesnot carry any coherent backscattering noise at f₀.

Because this interference process between main and backscattered signalsis coherent, only scatterers located along a segment of the coil 20centered on the coil's midpoint and along a length of the coil 20approximately equal to the coherence length of the source 40 contributeto the coherent backscattering. The scatterers located along the rest ofthe coil 20 produce a backscattered signal that is not temporallycoherent with the main signal, thereby producing intensity noise,instead of phase noise. This noise is considerably weaker than coherentbackscattering noise. In a Sagnac interferometer utilizing a broadbandsource, which has a short coherence length (typically tens of microns),the coherent backscattering noise is therefore very weak. As pointed outearlier, when such a source is used, the dominant noise of source istypically excess noise, not backscattering noise. On the other hand,utilizing a narrow-bandwidth laser source instead of a broadband sourcecan result in dramatically enhanced noise due to the greater portion ofthe optical fiber coil 20 that produces coherent backscattering noise,because the coherence length of the laser source (typically 1 cm orlonger, and usually much longer, up to thousands of km) is considerablylonger than that of a broadband source. The coherence length of thelaser source can be typically a fraction of the length of the opticalfiber coil 20 (e.g., 0.1% of the length of the coil 20, which can be afew hundred meters or longer) or longer. Therefore, all the scatterersalong the optical fiber coil 20 contribute to the coherentbackscattering noise.

In certain embodiments, this backscattering noise is advantageouslyreduced by sweeping or modulating the frequency of the laser source 40and filtering the detected signal. A linearly swept frequency v₁(t) ofthe laser source 40 is shown in FIG. 3A and can be expressed asv₁(t)=S·t, where S is the speed of the frequency sweep in Hz/s and t isthe time in seconds. As evident from FIG. 2, the main signal does notreturn from the coil 20 at the same time as does the backscatteredsignal. The delay Δt between the two depends on the position of thescatterer and can be expressed as Δt=n·(L−2z)/c, where z is the positionof the scatterer in the coil 20, L is the length of the coil 20, n isthe refractive index of the coil 20, and c is the speed of light.Consequently, at a given time, the backscattered and main signals havedifferent optical frequencies, as shown in FIG. 3B. Consequently, whenthey interfere, they produce a beat signal at the detector system 90with a frequency that is no longer at f₀ for most scatterers.Specifically, the signal that has traveled clockwise (cw) around thecoil 20 in FIG. 2, and the backscattered signal with which it interferes(which originates from backscattering of the counterclockwise signal),have both traveled through the phase modulator 130 when they interfere,so the frequency of their beat note is f₀+Δv_(B) where Δv_(B) can beexpressed as Δv_(B)=S·n·(L−2z)/c. In contrast, in the oppositedirection, at the output of the coil 20, the signal that has traveledcounterclockwise (ccw) around the coil 20 has gone through the phasemodulator 130, but the backscattered signal with which it interferes(which originates from backscattering of the cw signal) has not.Consequently, when they interfere, the frequency of their beat note isΔv_(B), i.e., it is not in the vicinity of f₀ but in the vicinity of dc.Thus, this beat note does not contribute to coherent backscatteringnoise around f₀. The frequency of the beat signal is indicative of theposition of the scatterer. The Fourier transform of the returningspectrum gives a spatial characterization of the scatterers along thecoil 20 relative to the center of the coil 20. Two scatterers whosepositions are symmetric relative to the center of the coil 20 are notdiscernible.

Thus, in certain embodiments, as a result of the combination of theconfiguration and the frequency modulation or sweep of the laserfrequency, the deleterious backscattering noise is modulated at a beatfrequency of f₀+Δv_(B) while the signal of interest is at frequency f₀.In other words, by sweeping the frequency of the laser source 40, theenergy in the backscattering noise is shifted to a frequency differentfrom the main signal frequency, thus allowing suppression of thebackscattered noise by spectral filtering. This filtering of the signalat the detector system 90 is performed at the output of the opticaldetector 92 by a band-pass or low-pass filter 94 centered at f₀ and witha cut-off bandwidth BW_(det) smaller than the beat frequency shiftΔv_(B). This filter does not transmit the noise beat note, therebyadvantageously reducing the contribution of backscattered noise to thesignal at the detection system 90. This filter 94 can comprise a lock-inamplifier, for example, or equivalent electronic filters. This type offilter is already used in existing FOGs to detect the rotation-inducedsignal at f₀ and to filter it from other sources of noise, so personsskilled in the art will know how to select an appropriate filter 94 inview of the disclosure herein. In certain embodiments in which thefiber-optic sensor 10 is used to sense dynamic perturbations (e.g.,acoustic waves), the cut-off bandwidth BW_(det) is selected to be higherthan the frequency of the perturbation. Cutoff bandwidth can be, forexample, in the range of a fractional Hz to a kHz or higher.

As shown in FIG. 4, for a given cut-off bandwidth BW_(det), the onlydeleterious scatterers are located within an equivalent coherence lengthL_(c) around the center of the coil 20, where L_(c) can be expressed asL_(c)=BW_(det)·c/(n·S). It is easy to make this effective lengthconsiderably shorter than the typical length of the coil 20. Forexample, for a bandwidth of 1 Hz and a sweep rate of 20 nm/s (which isstraightforward to accomplish), L_(c) is only 80 μm, independently ofthe actual coherence length of the source; this is true, for example,even if the coherence length of the source 40 is equal to the length ofthe coil 20, which can be hundreds of meters or even several kilometers.For coherent backscattering, the frequency-modulated laser source 40therefore appears to have a coherence length comparable to that of atypical SFS (e.g., a few tens of microns), even though its actualcoherence length may be longer by orders of magnitude.

This analysis illustrates that the backscattering noise reductionprovided by certain embodiments does not depend on the optical bandwidthover which the laser source 40 is swept, but only on S, the speed of thefrequency sweep. Therefore, in certain embodiments, it is advantageousto achieve a given rate S by utilizing a fast modulation of thefrequency of the laser source 40 over a small optical bandwidth. One ofthese advantages is that it is not required to sweep the laser frequencyover an optical bandwidth as wide as that of a broadband source. Inother embodiments, it is advantageous to achieve a given rate S byutilizing a low modulation of the frequency of the laser source 40 overa large optical bandwidth. This is advantageous when it is easier totune the laser over a large bandwidth at a low rate, as may be imposedfor example by the laser dynamics. For example, a distributed feedbackfiber laser exhibits slow relaxation frequencies (e.g., hundreds ofkHz), so in certain embodiments utilizing such a laser, it may bepreferable to sweep the frequency slowly over a large bandwidth.

As pointed out earlier, the important metric in how much the coherentbackscattered noise is reduced is the frequency sweep rate S. Sdetermines the frequency shift between the rotation-induced signalfrequency f₀ and the noise peak, which is shifted on both sides of f₀ asa result of the frequency modulation applied to the laser source 40.There are two locally optimum modes of operation of the sensor 10 interms of the value of S to select for use in certain embodiments. Inorder to decrease the backscattering noise at f₀ as much as possible,the noise peak can be shifted as far away from f₀ as possible. Incertain embodiments, the noise peak is shifted in a first mode ofoperation by selecting the frequency sweep rate S to be as large aspossible, resulting in a Δv_(B) that is much greater than f₀. In somelasers, this first mode of operation may be difficult to implement, forexample when the laser bandwidth is too small or the laser dynamic istoo slow, making it difficult or even impossible to accomplish a largesweep rate S. In certain embodiments, the sensor 10 can be operatedusing the rotation-induced signal at odd harmonics of f₀ (e.g., f₀, 3f₀,5f₀, etc.).

For these practical reasons, or for some other reasons, in certainembodiments, another mode of operation can be used. As the frequencymodulation is increased from 0, as described above, the noise peak at f₀is split into two peaks located on either side of f₀, namely atf₀±Δv_(B). But the same splitting occurs at all the noise peaks, whichare located at dc and all harmonics of f₀ (2f₀, 3f₀, etc.). Thus, thenoise peak that was originally at f₀ is frequency-shifted away from theuseful rotation-induced signal at f₀, but the noise peak that wasoriginally at dc is frequency-shifted towards f₀. The optimum modulationfrequency in this second mode of operation is to provide a beatfrequency Δv_(B)=f₀/2 (corresponding to S=c²/(4n²L²)). This second modeof operation is locally optimum because at this frequency shiftΔv_(B)=f₀/2, both the noise peak that was at dc and the noise peak thatwas at f₀ are frequency-shifted to f₀/2, i.e., midway between dc andsignal frequency f₀. Further increasing the modulation frequency (i.e.,above f₀/2) would move the original noise peak that was at f₀ furtheraway from f₀, which would reduce the noise at f₀, but it would also movethe original noise peak that was at dc closer to f₀, which wouldincrease the noise. Since the amplitude of the noise peak at dc isgreater than it is at f₀, the net result would be an increase inbackscattering noise at f₀. Therefore, the optimum rate in this secondmode of operation is S=c²/(4n²L²). For example, for a 200-m long fibercoil and a refractive index of 1.45, the condition on the sweep speed isS=268 GHz/s, or about 2.1 nm/s for a signal wavelength of 1.55 μm.Examples of laser sources 40 which can be used to provide this frequencysweep speed include, but are not limited to, an external-cavitysemiconductor diode laser (e.g, up to 100 nm/s).

For the first mode of operation, as the beat frequency is increased wellabove f₀, the noise peaks originally located at dc, f₀, and all higherharmonics of f₀, shift and spread out in frequency sufficient to overlapwith the signal peak at f₀. Two effects then contribute to the noiselevel at f₀. First, more noise peaks contribute to the noise at f₀,which increases the noise level at f₀. Second, the energy in the noisepeaks originally at f₀ and dc spreads out and loses amplitude at f₀,which decreases the noise level at f₀. Because the noise peaks at higherharmonics have amplitudes that decrease as the order of the harmonicsincreases, the first contribution is weaker than the second one, andtherefore the net effect of increase the increasing the frequency shiftto very high values is to decrease the noise at f₀.

FIGS. 5A and 5B illustrate a comparison of the optical linewidth of thelaser source 40 and the electrical linewidth of the beat signal. Asshown in FIG. 5A, the laser source 40 has an optical frequency v₁ and anoptical linewidth δv₁. The spectral linewidth of the beat signal betweentwo uncorrelated lasers operating at different optical frequencies isthe sum of the linewidths of the lasers. However, the beat signallinewidth tends to zero if the laser signals are correlated. In thecontext of the fiber-optic sensor 10 shown in FIG. 2, the two beatingoptical signals are correlated when the delay between these signals isshorter than the coherence time of the laser source 40. Therefore, incertain embodiments in which the laser coherence length is longer thanthe coil 20, the backscattered and the main signals are correlated, andthe beat signal will present an electrical linewidth significantlysmaller than the optical linewidth δv₁ of the laser source 40, as shownby the solid line in FIG. 5B. The dashed line in FIG. 5B illustrates aworst-case scenario in which the beat signals are uncorrelated,resulting in a linewidth of 2δv₁.

FIGS. 5C-5E illustrate the proper frequency f₀ and the beat frequencyΔv_(B) for various levels of coherence of the laser source 40. For ahighly coherent laser source 40 (L_(c)>>L, as shown in FIG. 5C), thebeat signals between the return signals and the coherent backscatteredsignals is very narrow, and filtering can yield a high noisesuppression. As the coherence length drops (as shown in FIGS. 5D and5E), the beat signals broaden, and they overlap increasingly at f₀, andthe noise suppression is less effective.

In certain embodiments in which the linewidth of the beat signal is lessthan the beat frequency Δv_(B), the backscattering noise can be filteredout using a low-pass filter (e.g., a filter having a cut-off bandwidthBW_(det)) or a bandpass filter. Therefore, in certain embodiments, thelaser source 40 has a coherence length larger than the coil 20, suchthat the linewidth of the beat signal is reduced, and the backscatteringnoise in the resultant signal can be more effectively reduced byspectral filtering. For example, for a 200-m long fiber coil, thecondition that the optical linewidth δv₁ be much less than c/L issatisfied by having δv₁<<1.5 MHz. Such optical linewidths can beprovided by external-cavity semiconductor diode lasers (typically havinglinewidths of a few hundreds of kHz) or single-mode fiber lasers(typically having linewidths of a few tens of kHz).

The frequency of the laser source 40 cannot be infinitely increased, soin certain embodiments, a periodic modulation is applied (e.g., asawtooth frequency modulation waveform shape as illustrated in FIG. 6A).The frequency f_(sweep) of this frequency modulation in certainembodiments is advantageously selected to be much higher than the filterbandwidth BW_(det) of the detection system 90. As illustrated by FIG.6B, for periodic frequency modulation, the beat frequency Δv_(B) betweenthe main signal and the backscattered signal tends to zero around thewrapping portions of the frequency modulation (specifically, at any ofthe points where the backscattered curve and the main curve cross in thetop graph of FIG. 6B), since it is near these intersection points thatthe returning main signal and the returning backscattered signal havesubstantially equal frequencies. Consequently, the reduction of the beatfrequency in the vicinity of these points effectively moves part of thebackscattering noise into the detection bandwidth, thus increasing theremaining backscattering noise at these points. The magnitude of thisunfiltered noise can be reduced in certain embodiments by increasing theoptical bandwidth over which the laser source 40 is swept, thusincreasing the duty cycle of the time dependence of the beat frequency,or equivalently reducing the number of intersection points per unittime. The higher the bandwidth, the fewer the number of wrappings (orcrossing points) per unit time, and thus the greater the noisereduction.

Examples of laser sources 40 compatible with certain such embodimentsinclude, but are not limited to, external-cavity semiconductor diodelasers (e.g., which can be swept by 100 nm) and distributed-feedbackfiber lasers (e.g., which can be swept at high speed usingpiezo-electric ceramics by over 10 nm by stretching the fiber, and over90 nm by compression of the fiber). For example, the frequencymodulation of the laser source 40 can be provided by using anarrow-linewidth (e.g., a single-frequency) semiconductor laser diode,of which several varieties exist, and by modulating the laser-diodedrive current. This is well known to produce a slight modulation of thelaser frequency, at the frequency applied to the drive current. Thisfrequency controls the sweep rate, while the amplitude of the currentmodulation controls the amplitude of the laser frequency modulation.

Other frequency modulation waveform shapes (e.g, sinusoidal) are alsocompatible with certain embodiments described herein. In certainembodiments, the frequency modulation waveform shape is chosen to have aflat density of probability (e.g., as does a sawtooth). FIG. 7 comparesthe density of probability of a sawtooth waveform and a sinusoidalwaveform. The sinusoidal frequency modulation waveform shape woulddramatically increase the magnitude of the backscattering noise sinceits density of probability is largest near the extrema of the sinewaveform.

FIG. 8A schematically illustrates an example sensor 100 in accordancewith certain embodiments described herein. The sensor 100 of FIG. 8A isanother example of a fiber-optic gyroscope comprising a standard Sagnacloop which comprises the coil 20. The sensor 100 of FIG. 8 can be a FOGin the minimum configuration (see, e.g., H. C. Lefèvre, “The Fiber-OpticGyroscope,” Artech House, Inc., Norwood, Mass. (1993)). Light from thelaser source 40 is transmitted to the optical circulator 80, through apolarizer 110, to the optical coupler 70 which is closed upon itself bya polarization controller 120, the optical fiber coil 20, and anelectro-optic (EO) phase modulator 130. The phase modulator 130 can beused to bias the sensor 100 in quadrature, thus improving thesensitivity of the sensor 100. In certain embodiments, the polarizer 110and the phase modulator 130 are fiber-based or fiber-pigtailedcomponents which are commercially available from a number of vendors andmanufacturers (e.g., JDS Uniphase Corp. of Milpitas, Calif.).

FIG. 8B schematically illustrates an example sensor 102 in accordancewith certain embodiments described herein. The sensor 102 of FIG. 8B isanother example of a fiber-optic gyroscope comprising a standard Sagnacloop which comprises the coil 20. The sensor 102 comprises apolarization-maintaining (PM) fiber downstream from the polarizer 110(e.g., in the coil 20, between the polarizer 110 and the first opticalcoupler 70, and/or within the first optical coupler 70). In certain suchembodiments, the entire optical path downstream from the polarizer 110is PM fiber. In certain embodiments, the sensor 102 utilizes PM fiberthroughout (i.e., downstream from the source 40). By utilizing PM fibereither along the entire optical path downstream from the polarizer 110or throughout the sensor 102, certain embodiments obviate the use of thepolarization controller 120 of the sensor 100. Certain such embodimentsadvantageously avoid the need to adjust the polarization controller 120(either manually, which cannot be done for an actual FOG, or withcomplicated feedback systems, which add cost and complexity). The phasemodulator 130 of certain embodiments is driven by a function generator140 which is coupled to a lock-in amplifier 150 which outputs a signalto a computer system 160. The lock-in detection at the proper frequencyof the sensor 100 in certain embodiments can advantageously improve thesignal-to-noise ratio. With this phase modulation, the returning signalof interest is centered at the frequency of the phase modulation (i.e.,at the proper frequency f₀).

In a manner similar to that discussed above with regard to the exampleconfiguration illustrated by FIG. 2, for the sensor 100 schematicallyillustrated by FIG. 8, the backscattered light due to only one of thecounterpropagating signals propagates through the phase modulator 130.For example, for the first signal 52 propagating through thepolarization controller 120 then through the rest of the coil 20 andthen through the phase modulator 130, any backscattered light producedwithin the coil 20 will propagate towards the polarization controller120 and away from the phase modulator 130 before reaching the firstoptical coupler 70. Conversely, for the second signal 56 propagatingthrough the phase modulator 130, then through the coil 20, and thenthrough the polarization controller 120, any backscattered lightproduced within the coil 20 will propagate through the phase modulator130 before reaching the first optical coupler 70. The backscatteredlight that does not propagate through the phase modulator 130 is thusnot phase modulated, and therefore does not contribute to thebackscattering noise at the detection frequency. Such a configuration isdifferent from other configurations (e.g., J. Zheng, “All-fibersingle-mode fiber frequency-modulated continuous-wave Sagnac gyroscope,”Optics Letters, Vol. 30, pp. 17-19 (2005) and J. Zheng, “Differentialbirefringent fiber frequency-modulated continuous-wave Sagnacgyroscope,” IEEE Photonics Technology Letters, Vol. 17, pp. 1498-1500(2005)) in which both backscattered signals are modulated so bothcontribute to the noise.

In addition, for the sensors 100, 102 schematically illustrated by FIGS.8A and 8B, as well as the sensor 10 schematically illustrated by FIG. 1,both of the counterpropagating signals are frequency-modulated and arecombined together to produce the third signal 60. Other configurations(e.g., B. Culshaw et al., “Frequency Modulated Heterodyne Optical FiberSagnac Inteferometer,” IEEE Trans. Microwave Theory and Technique, Vol.MTT-30, pp. 536-539 (1982)) do not modulate the frequency of the twocounterpropagating signals of the coil 20 and combine these signalstogether.

Experimental results are provided below for the example sensor 100 ofFIG. 8A with two different FOGs, each one utilizing a different opticalfiber: a 200-m long standard optical fiber (SMF-28 fiber from Corning,Inc.) wound on an 8-cm-diameter spool, and a 235-m long air-corephotonic-bandgap fiber (HC-1550-02 fiber from Crystal Fibre) wound on an8-cm-diameter spool. The performance of the FOGs was studied by usingtwo different optical sources: a standard erbium-doped superfluorescentfiber source (for the purpose of gathering baseline noise data), and a200-kHz-linewidth external-cavity tunable laser. The frequency of thelaser could be swept using frequency modulation (FM). In this case, thedriving current of the laser was modulated, which produced a very smallwavelength modulation bandwidth (estimated to be 1 pm). Alternatively,the laser frequency could be swept using a frequency sweep (FS), inwhich case the laser frequency was swept by tuning the external cavityof the semiconductor laser, consisting of an optical grating. Thisapproach offered a wide optical modulation bandwidth (up to 100 nm).

FIG. 9 illustrates the rotation signal for the sensor 100 with an SMF-28fiber coil observed at the output of the lock-in amplifier 150 for threedifferent optical sources: an SFS, a laser, and a frequency-modulatedlaser. The EO phase modulator 130 was driven by a sine wave from thefunction generator 140 at 400 kHz, the optical power returning to thedetector 92 was −20 dBm, and the equivalent integration time of thelock-in amplifier 150 was 1.28 s (BW_(det) of 0.78 Hz). The data of FIG.9 were taken with the sensor 100 at rest and over a period of timeapproximately equal to ten times the equivalent integration time. Asshown by FIG. 9, the noise with the SFS is much smaller than the noiseof the laser, respectively 3°/h and 33°/h at one sigma. The increasednoise observed when interrogating this FOG with the laser is due tobackscattering, while the noise observed with the SFS is dominated byexcess noise.

For the frequency-modulated laser, the laser frequency was modulated byapplying sawtooth modulation to the laser driving current, at 8 kHz witha peak-to-peak amplitude of 1 mA. The amplitude of the frequencymodulation was estimated to be 1 pm, and the frequency sweep speed S wasestimated to be 4.4 nm/s. The frequency-modulated laser considerablyreduced the backscattering noise to 7.6°/h as compared to the 33°/h ofthe non-frequency-modulated laser, about a factor of 4 improvement. Asexplained above, the reason for this improvement is that thebackscattering noise is shifted off the proper frequency f₀ and filteredout by the lock-in amplifier, and the noise at f₀ drops. The shift isproportional to the frequency sweep speed S; the frequency shift equals40 kHz for modulation at 1 kHz, and it equals about 140 kHz at 4 kHz.These experimental results therefore support the reduction of thebackscattering noise by a frequency-swept laser. The amplitude noise ofthe laser used in FIG. 9 at the frequency of interest f₀ limits theperformance of this sensor 100 in certain embodiments. A laser withlower noise would offer similar or better performance than the SFS incertain other embodiments, since a laser presents limited excess noisein comparison to a broadband source. In addition, FIG. 9 illustratesthat a frequency-modulation of the laser over a very small (1 pm)optical bandwidth is sufficient to dramatically reduce thebackscattering noise in the sensor 100.

FIG. 10 illustrates the RF spectrum observed at the output of thedetector 92 for the sensor 100 with an SMF-28 fiber at rest. Thisspectrum agrees qualitatively well with the spectrum expected inaccordance with FIG. 5B. When an SFS is used as the FOG source 40, thebackscattering noise component observed at f₀ is very small. When theSFS is replaced with the laser source, strong backscattering noise isobserved at f₀. By modulating the frequency of the laser, FIG. 9 showsthat the backscattering noise is shifted away from, and on both sidesof, the phase modulation frequency f₀. This frequency shift of thebackscattering noise was observed around every multiple (zero included)of f₀. The laser frequency modulation clearly reduces the backscatteringnoise, although not sufficiently to reach the low noise level of thesame FOG operated with an SFS (see FIG. 10). As described above, thisfrequency shift was observed to be proportional to the frequency sweepspeed. FIG. 10 also shows that the backscattering reduction is limitedin certain embodiments. The backscattering noise peaks can not beshifted further than the phase modulation frequency (i.e., Δv_(a) mustbe smaller than f₀), or the noise shifted from the dc towards positivefrequencies will be observed at the frequency of interest f₀. Incontrast, in certain other embodiments, the backscattering noise isshifted much further to high frequencies by sweeping the frequency ofthe laser at a very high rate so that Δv_(B)>>f₀, as explained furtherbelow. For example, rotation of the grating of the external cavity ofthe semiconductor laser can be used to obtain frequency rate as high as100 nm/s.

The beat signal was observed to have a 50-kHz linewidth. As discussedearlier, this linewidth is smaller than twice the optical linewidth ofthe laser. Consequently, the beating waves are likely to be partiallycorrelated, which is in good agreement with the 1.5-km coherence lengthof the laser.

Similar trends were observed for the sensor 100 utilizing the air-coreoptical fiber coil 20. The EO phase modulator 130 was driven with a sinewave at 632 kHz, the optical power returning to the detector 92 was −24dBm, and the equivalent integration time of the lock-in amplifier 150was 1.28 s (BW_(det) of 0.78 Hz). FIG. 11 illustrates the RF spectraobserved at the output of the detector 92. The main difference comparedto the RF spectra for the SMF-28 fiber coil 20 of FIG. 10 is theenhanced (factor of 10) backscattering noise by 20 dB. (electrical), dueto the enhanced backscattering coefficient in the air-core optical fiberin comparison to a standard fiber. The laser frequency modulationreduces the backscattering noise, just as it did with the standard fibercoil, but also not enough to reach the low-noise performance of the SFS.When the laser frequency was modulated at 3.2 kHz, and at a speed suchthat the frequency rate was S≈1.8 nm/s (or 232 GHz/s), the noise wasobserved to be 264°/h, which is roughly 30 times the noise of 7.7°/hobserved with the SFS. The noise magnitude was measured at one sigmaover 10 times the equivalent integration time of the lock-in amplifier150. This rate S induced a frequency shift in the noise peak of ˜80 kHz(see FIG. 11). Although this noise shift is not as high as the optimumfrequency of f₀/2 according to the second mode of operation describedabove, the conditions under which this FOG was tested, and the reductionin noise it produced, provide an illustration of the second mode ofoperation. This embodiment demonstrates a significant reduction of thebackscattering noise in an air-core FOG in this second mode ofoperation.

As described above, the first mode of operation includes modulating thefrequency at a much higher rate than in the second mode of operation.The backscattering noise for either an air-core or a conventionaloptical fiber coil 20 is then shifted to much higher frequencies(Δv_(B)>>f₀) by sweeping the frequency of the laser at a very high rate(e.g., as high as 100 nm/s). This can be accomplished in practice, e.g.,by rotating the grating of the external cavity of the semiconductorlaser. In this case, as described above, the energy in all of the noisepeaks in the vicinity of all the harmonics of f₀ is spread out over avery large frequency range, and very little overlaps with the frequencyof interest f₀. In the experiment that aimed to prove this point, thedetected optical power was −20 dBm, the lock-in equivalent integrationtime was 38 s, and the laser frequency was swept over 30 nm at a speedof 100 nm/s with a sawtooth shape. The laser was amplified with anerbium-doped fiber amplifier. The observed noise of the air-core FOGdriven by the frequency-swept source was 16°/h (measured at one sigmaover 100 s), which is only 3 times the noise observed with the SFS(5.2°/h). The noise was independent of the optical bandwidth: sweepingthe laser frequency over 10 nm or 60 nm did not significantly change thenoise magnitude. In addition, this performance was obtained despiteoptical power fluctuations as high as 5 dB, which were caused by thefact that the length of fiber between the laser and the input/outputpolarizer of the FOG did not maintain polarization.

FIGS. 12A and 12B present some temporal and spectral characteristics ofthe detector signal for the air-core FOG at rest. When the FOG is drivenby an SFS, the detected signal is the expected component at 2f₀, as seenin the top graph of FIG. 12A. When the SFS is replaced by the laser,this component is hidden by the backscattering noise, as seen in themiddle graph of FIG. 12A. With the frequency-swept laser, the expectedcomponent at 2f₀ is observed, with over-modulation due to thebackscatter beat noise (see in the bottom graph of FIG. 12A). FromΔv_(B)=S·n·(L−2z)/c, and assuming the average position of the scatterersis z=0 (or L, since 0 and L are the two positions where scattererscontribute the most to the noise), the expected beat frequency is 9.7MHz, which is in very good agreement with the 9 MHz maximum observedwith the RF spectrum analyzer, as shown in FIG. 12B.

FIG. 13 presents the measured dependence of the noise on the square rootof the detection bandwidth for the FOG using the SMF-28 fiber in thecoil 20. As discussed above, the integration time of the lock-inamplifier 150 in certain embodiments is advantageously selected to belarge compared to the period of the frequency sweep. FIG. 13 illustratesthe importance of the ratio between the detection bandwidth of thelock-in amplifier 150 and the sweep rate of the laser source 40. In arandom-walk regime, the expected linear dependence for the laser-drivenand the SFS-driven FOG were observed. In addition, the noise with thefrequency-swept laser was observed to be as high as in the laser-drivenFOG for large bandwidth, and to approach the noise of the broadbandsource for smaller detection bandwidth.

As described herein, a frequency-swept narrow-band laser (e.g., adistributed feedback fiber laser) can advantageously be used in a fiberoptic sensor (e.g., a FOG). The backscattering noise can be reduced(e.g., by a factor of 4) in certain embodiments compared to alaser-driven FOG. Punctual reflections in the coil 20 can cause coherentbackscattering noise, which can be reduced by frequency-modulating thelaser, so the backscattering noise can be reduced further (e.g., by afactor of 10) by removing sources of reflections in the FOG (e.g., byreplacing fiber connectors with fusion splices at all the fiber-to-fiberconnections). Frequency-modulating the laser source 40 can also reducecoherent noise arising from interference between one or both of the main(or primary) signals and reflections occurring at punctual interfacesalong the Sagnac loop. Such reflections include, but are not limited to,spurious reflections at a fiber-to-fiber-splice, Fresnel reflection atinternal interfaces inside a component (e.g., the phase modulator)located in the coil 20, or Fresnel reflection at the optical connectionbetween the fiber and the EO modulator chip, for example when the chipis a LiNbO₃ chip.

With a standard optical fiber, the noise performance of the FOG drivenby the frequency-swept narrow-band laser is almost as good as with abroadband source. The use of a frequency-swept narrow-band laser incertain embodiments advantageously provides an improved sensitivity(e.g., reduced noise) and improved stability (e.g., mean wavelengthstability) for all FOGs driven with a laser. The further use of anair-core fiber affords the additional advantages of an improved thermalstability, a reduced Kerr-induced phase drift, and a reduced sensitivityto magnetic fields. The backscatter noise reduction of certainembodiments mainly depends on the frequency-sweep speed, and sweepingthe laser frequency over only 1 pm was sufficient to achieve substantialreduction of the backscatter noise. Certain embodiments described hereinallow easier control of the mean wavelength of the laser source incomparison to a broadband source, thus offering better long-termstability for the FOG scale factor.

FIG. 14 schematically illustrates an example sensor 170 in accordancewith certain embodiments described herein. The sensor 170 of FIG. 14 isanother example of a fiber-optic gyroscope comprising a standard Sagnacloop which comprises the coil 20. The sensor 170 of FIG. 14 is anintegrated optic chip in which the FOG components are all made on a chip(LiNbO₃), in accordance with the standard method to make a commercial.FOG. In certain such embodiments, the key components of the sensor 180,including but not limited to the first optical coupler 70 (e.g., a Yjunction), the second optical coupler 80 (e.g., a Y junction), thepolarizer 110, and the phase modulator 130, are all fabricated usingstandard technology on the same integrated optic chip, for example onLiNbO₃, which presents certain well-recognized advantages ofcompactness, mechanical stability, and ease and reduced cost oflarge-scale manufacturing. In certain embodiments, the coil 20 comprisesa polarization-maintaining fiber. In certain other embodiments, apolarization controller can be positioned at a point along the coil 20to control the birefringence of the coil 20 and ensure that the signaloutput state of polarization is alighed with respect with the polarizertransmission axis, thereby providing polarization reciprocity. Incertain embodiments, the coil 20 comprises an air-core fiber.

In certain embodiments, this frequency modulation described herein canbe used with many other implementations of the basic FOG configurationsand regardless of the specific technologies used to fabricate thecomponents or the manner in which the FOG is operated. For example,frequency modulation can be used whether the FOG is operated open loopor closed loop, independently of the exact scheme used to close theloop, and independently of the modulation scheme or any other signalprocessing scheme implemented in the FOG as a whole for any purpose.

FIG. 15 is a flow diagram of an example method 200 of operating afiber-optic sensor in accordance with certain embodiments describedherein. The method 200 comprising providing a fiber-optic sensorcomprising an optical fiber coil and a laser source optically coupled tothe coil in an operational block 210. The method 200 further comprisestransmitting light from the source to the coil as a first signal and asecond signal in an operational block 220. The first signal propagatesalong the coil in a first direction and the second signal propagatesalong the coil in a second direction opposite to the first direction.The optical paths of the first signal and the second signal aresubstantially reciprocal with one another. The method 200 furthercomprises combining the first signal and the second signal together togenerate a third signal in an operational block 230. The method 200further comprises modulating a frequency of the laser source such thatthe first signal and the second signal are frequency-modulated in anoperational block 240. In certain embodiments, the third signalcomprises a backscattering noise portion and a remaining portion, andmodulating the frequency of the laser source shifts the backscatteringnoise portion to at a beat frequency different from a frequency of theremaining portion.

Of the possible effects that cause the error signal due tobackscattering to fluctuate, the primary contribution is random phasefluctuations in the source. The other contributions, such as temperaturetransients in the fiber, have a much longer characteristic time constantand will generally lead to drift in the FOG signal output over time,rather than a random walk noise (see for example K. Kråkenes and K.Bløtekjaer, Effect of Laser Phase Noise in Sagnac Interferometers,Journal of Lightwave Technology, Vol. 11, No. 4, April 1993). Asdescribed above, the primary approach to reduce the effect of coherentbackscattering noise has previously been to use a broadband source tointerrogate the FOG. Coherent backscattering noise is reduced when usinga broadband source because the source coherence length L_(c) is thenvery short compared to the length of the coil. As a result, only lightscattered by scatterers located within approximately one coherencelength of fiber centered at the coil halfway point contributes tocoherent backscattering noise. Light scattered by scatterers locatedoutside this region has a delay relative to the primary wave that islonger than the source coherence time and interferes incoherently, thusit does not contribute to significant fluctuations in the error signal.Therefore, in order to reduce the error due to scattering, one approachis to make the region of fiber that contributes to the coherentbackscattering smaller and smaller by reducing the coherence length ofthe source, or, equivalently, using a broadband light source. For abroadband source this region is generally only a few microns or tens ofmicrons in length.

Another approach to reduce the RMS fluctuations in the error signal dueto coherent backscattering and reflections (e.g., punctual reflections)in accordance with certain embodiments described herein is to use ahighly coherent source, i.e., a source with a coherence length longerthan the coil length. From the discussion above, increasing the sourcecoherence length increases the length of fiber that contributes tocoherent backscattering noise, and it therefore generally leads to alarger backscattering noise and thus a larger FOG random walk. However,the backscattering noise increases only up to the point where thecoherence length of the source is equal to the length of the coil. Thisincrease is of course due to the fact that more scatterers contribute tocoherent scattering noise. But when the coherence length of the sourceis increased beyond the length of the coil, two effects take place.First, the length of fiber that contributes to coherent backscatteringnoise no longer increases, because all the scatterers along the entirecoil fiber already contribute to coherent backscattering noise. Second,increasing the coherence length of the source leads to smaller andsmaller random phase fluctuations in the photons emitted by the source.Since these fluctuations are what ultimately gives rise to thefluctuations in the error signal, the fluctuations in the backscatteringnoise decrease, and so does the random walk. Therefore, since the regionthat contributes coherently to the backscattered signal is now fixed andthe random phase fluctuations of the source can be made smaller byincreasing the coherence length, the RMS fluctuations in the errorsignal also decrease. This leads to a reduction in the FOG random walkdue to coherent backscattering, and a concomitant improvement in theminimum detectable rotation rate. Certain such embodiments can be usedwith various sensor configurations, including but not limited to thoseof FIGS. 1, 2, 8A, 8B, and 14.

FIG. 16 shows the results of a numerical theoretical model used toverify the above-described principle. The model was used to numericallysimulate the interactions between the random phase fluctuations of asource with the local inhomogeneities in the fiber loop for variouscoherence lengths. FIG. 16 shows the results of this simulation for oneparticular coil consisting of 255 meters of fiber with statisticalproperties equivalent to SMF-28 fiber, investigating the effects onnoise for only one random distribution of scatterers. The numericalmodel can also average the phase noise (and the corresponding randomwalk) over all possible scatterers distributions, for which the modelwould yield the same curve but with a slightly different shape andvertical axis absolute scale (not shown for clarity). The verticaldashed line indicates the coherence length equal to the coil length(L_(c)=L). As shown in FIG. 16, the FOG random walk is relatively smallfor sources with a short coherence length. As the coherence length isincreased, the random walk also initially increases. Once the coherencelength exceeds the length of the coil, however, the random walk due tocoherent backscattering decreases, as described above.

The validity of this model was confirmed with the experimentaldemonstration of a fiber optic gyroscope driven by a frequency-modulatedlaser and with parameters matching those used in the simulation. Theexperimental configuration utilized an external cavity laser with a200-kHz full-width-at-half-maximum linewidth (or a coherence length ofabout 1.5 km) coupled into a minimum configuration FOG, as shown in FIG.8A, with a 240-meter coil of SMF-28 fiber. The FOG was biased at theproper coil frequency with a fiber-pigtailed electro-optic phasemodulator 130. The returning signal was measured with a P-I-N photodiodeand demodulated using a lock-in amplifier with a bandwidth of 1 kHz.This experimental configuration exhibited a FOG random walk of 0.49deg/√hr. The numerical model predicted an average random walk of 0.45deg/√hr, calculated over all possible scatterers distributions, showingvery close agreement with our experimental results with one particularfiber and confirming the validity of the simulations.

FIG. 16 shows that in principle, the coherence length of the source incertain embodiments can be selected to be as long as possible to reducethe backscattering noise as much as possible. For example, increasingthe coherence length to about 150 kilometers will result in a coherentbackscattering noise reduction of a factor of 15 from its peak value.The reduction is roughly linear on a log-log scale, so the net noisereduction can be characterized, again in the particular example of thisfiber, by a factor of ten every time the coherence length is increasedby a factor of 200. In certain embodiments, however, it can besufficient to reduce the backscattering noise to just below the nextdominant source of noise, for example shot noise.

The numerical model used to generate these results of FIG. 16 did nottake into account other sources of phase noise that might be present ina light source when its degree of coherence becomes extremely high. Suchsources of noise include spontaneous emission noise, relative intensitynoise (RIN), and excess noise. When these sources of noise are present,the curve in FIG. 16 no longer drops indefinitely in the L_(c)>L region.Instead, above some critical coherence length the curve stops decreasingand likely levels off to an asymptotic value. This asymptotic levelcorresponds to the maximum amount of coherent backscattering noisereduction possible with L_(c)>L and this particular source. The amountof noise reduction achievable with a given source can easily be measuredwith a fiber optic gyroscope, as described above in relation to theexperimental results described above.

Because the random walk initially increases with increasing coherencelength, most previously-existing noise reduction schemes have focused onreducing the source coherence length. Previous work has not consideredthe regime when the coherence length is much longer than the length ofthe loop and has not predicted the performance described above. Becauseof the advantages of narrowband sources discussed above, such as stablecenter wavelength and negligible excess noise, certain embodimentsutilizing a FOG with a highly coherent source (i.e., a source with acoherence length that exceeds the coil length) offers significantadvantages over more traditional methods.

In certain embodiments, a ratio of the coherence length to the length ofthe coil is greater than 1, greater than 1.1, greater than 1.5, greaterthan 2, greater than 5, greater than 10, greater than 100, or greaterthan 1000. In certain embodiments, the fiber-optic sensor utilizes bothfrequency modulation and a coherence length longer than the length ofthe coil. In certain other embodiments, the fiber-optic sensor utilizeseither frequency modulation or a coherence length longer than the lengthof the coil.

FIG. 17 is a flow diagram of an example method 300 of operating afiber-optic sensor in accordance with certain embodiments describedherein. The method 300 comprising providing a fiber-optic sensorcomprising a coil of optical fiber having a length and a laser sourceoptically coupled to the coil fiber in an operational block 310. Thelaser source is selected to have a coherence length greater than thelength of the coil fiber. The method 300 further comprises transmittinglight from the source to the coil as a first signal and a second signalin an operational block 320. The first signal propagates along the coilin a first direction and the second signal propagates along the coil ina second direction opposite to the first direction. The optical paths ofthe first signal and the second signal are substantially reciprocal withone another. The method 300 further comprises combining the first signaland the second signal together to generate a third signal in anoperational block 330.

Various embodiments have been described above. Although the inventionhas been described with reference to these specific embodiments, thedescriptions are intended to be illustrative of the invention and arenot intended to be limiting. Various modifications and applications mayoccur to those skilled in the art without departing from the true spiritand scope of the invention as defined in the appended claims.

1. A fiber-optic sensor comprising: an optical fiber coil; and afrequency-modulated laser source optically coupled to the coil, whereinlight from the source is transmitted to the coil as a first signalpropagating along the coil in a first direction and a second signalpropagating along the coil in a second direction opposite to the firstdirection, wherein the optical paths of the first signal and the secondsignal are substantially reciprocal with one another and the firstsignal and the second signal are combined together after propagatingthrough the coil to generate a third signal.
 2. The sensor of claim 1,wherein the sensor is a Sagnac-based fiber-optic gyroscope and the thirdsignal is indicative of rotations of the coil.
 3. The sensor of claim 1,further comprising at least one optical coupler between and opticallycoupled to the coil and to the laser source.
 4. The sensor of claim 3,wherein the at least one optical coupler comprises a first opticalcoupler comprising a first port, a second port, and a third port, thefirst port receiving light generated by the laser source, the secondport optically coupled to a first end of the coil and the third portoptically coupled to a second end of the coil.
 5. The sensor of claim 4,wherein the first signal is transmitted by the second port to the firstend of the coil to propagate in the first direction along the coil andis transmitted by the second end of the coil and the third port to thefirst port, and the second signal is transmitted by the third port tothe second end of the coil to propagate in the second direction alongthe coil and is transmitted by the first end of the coil and the secondport to the first port.
 6. The sensor of claim 4, wherein the firstoptical coupler comprises a 3-dB optical coupler.
 7. The sensor of claim4, wherein the at least one optical coupler further comprises a secondoptical coupler comprising a first port, a second port, and a thirdport, the first port receiving light generated by the laser source, thesecond port optically coupled to the first port of the first opticalcoupler, and the third port optically coupled to a detection system. 8.The sensor of claim 7, wherein light from the laser source received bythe first port of the second optical coupler is transmitted through thesecond port of the second optical coupler to the first port of the firstoptical coupler, and the third signal received from the first port ofthe first optical coupler by the second port of the second opticalcoupler is transmitted through the third port of the second opticalcoupler to the detection system.
 9. The sensor of claim 7, wherein thesecond optical coupler comprises an optical circulator.
 10. The sensorof claim 3, further comprising a polarization controller between andoptically coupled to the at least one optical coupler and the opticalfiber coil.
 11. The sensor of claim 3, further comprising a phasemodulator between and optically coupled to the at least one opticalcoupler and the optical fiber coil.
 12. The sensor of claim 11, furthercomprising a function generator and a detection system comprising: adetector configured to receive the third signal; and a lock-in-amplifierconfigured to receive an output from the detector, wherein the phasemodulator is driven by the function generator, and the lock-in amplifieris coupled to the function generator.
 13. The sensor of claim 1, whereinthe optical fiber coil comprises an air-core photonic-bandgap fiber. 14.The sensor of claim 1, wherein the laser source comprises anexternal-cavity semiconductor diode laser or a distributed feedbackfiber laser.
 15. The sensor of claim 1, wherein the frequency modulationof the laser source has a periodic sawtooth waveform shape.
 16. Thesensor of claim 1, further comprising a detection system configured toreceive the third signal, the detection system comprising a filterbandwidth, wherein the third signal comprises a backscattering noiseportion and a remaining portion, and the filter bandwidth is selected tofilter out the backscattering noise portion.
 17. The sensor of claim 1,wherein the sensor is a fiber-optic gyroscope comprising a standardSagnac loop which comprises the coil.
 18. A method of operating afiber-optic sensor, the method comprising: providing a fiber-opticsensor comprising an optical fiber coil and a laser source opticallycoupled to the coil; transmitting light from the source to the coil as afirst signal and a second signal, the first signal propagating along thecoil in a first direction and the second signal propagating along thecoil in a second direction opposite to the first direction, wherein theoptical paths of the first signal and the second signal aresubstantially reciprocal with one another; combining the first signaland the second signal together to generate a third signal; andmodulating a frequency of the laser source such that the first signaland the second signal are frequency-modulated.
 19. The method of claim18, wherein the third signal comprises a backscattering noise portionand a remaining portion, and modulating the frequency of the lasersource shifts the backscattering noise portion to at a beat frequencydifferent from a frequency of the remaining portion.
 20. A fiber-opticsensor comprising: a coil of optical fiber having a length; and a lasersource optically coupled to the coil, the laser source having acoherence length longer than the length of the coil fiber, wherein lightfrom the source is transmitted to the coil as a first signal propagatingalong the coil in a first direction and a second signal propagatingalong the coil in a second direction opposite to the first direction,wherein the optical paths of the first signal and the second signal aresubstantially reciprocal with one another and the first signal and thesecond signal are combined together after propagating through the coilto generate a third signal.
 21. The sensor of claim 20, wherein thesensor is a fiber-optic gyroscope comprising a standard Sagnac loopwhich comprises the coil.
 22. The sensor of claim 20, wherein a ratio ofthe coherence length to the length of the coil fiber is greater than 1.23. The sensor of claim 20, wherein a ratio of the coherence length tothe length of the coil fiber is greater than 1.1.
 24. The sensor ofclaim 20, wherein a ratio of the coherence length to the length of thecoil fiber is greater than 1.5.
 25. The sensor of claim 20, wherein aratio of the coherence length to the length of the coil fiber is greaterthan
 2. 26. The sensor of claim 20, wherein a ratio of the coherencelength to the length of the coil fiber is greater than
 5. 27. The sensorof claim 20, wherein a ratio of the coherence length to the length ofthe coil fiber is greater than
 10. 28. The sensor of claim 20, wherein aratio of the coherence length to the length of the coil fiber is greaterthan
 100. 29. The sensor of claim 20, wherein a ratio of the coherencelength to the length of the coil fiber is greater than
 1000. 30. Amethod of operating a fiber-optic sensor, the method comprising:providing a fiber-optic sensor comprising a coil of optical fiber havinga length and a laser source optically coupled to the coil, the lasersource having a coherence length longer than the length of the coilfiber; transmitting light from the source to the coil as a first signaland a second signal, the first signal propagating along the coil in afirst direction and the second signal propagating along the coil in asecond direction opposite to the first direction, wherein the opticalpaths of the first signal and the second signal are substantiallyreciprocal with one another; and combining the first signal and thesecond signal together to generate a third signal.